Observational studies have been attributed some of the energetic (>50 keV) particles observed at various sites near the bow shock and in the magnetosheath to a magnetospheric source. A large-scale picture of the spatial distribution of these particles in the magnetosheath is difficult to obtain from the data because of constantly changing interplanetary conditions. Here an approximate picture of the volumes occupied by particles that origiinate in the vicinity of the magnetopause is obtained by mapping magnetosheath magnetic field lines which drape over the magnetopause through the bow shock. Subsets of these field lines that connect to potential sites of magnetic merging on the magnetopause are also traced in the event that the particle leakage occurs preferentially where normal components of the field are present across the boundary. The results of this modeling exercise suggest that energetic magnetospheric particles which are not scattered by magnetosheath magnetic fluctuations are likely to exit the magnetosheath in the region of the quasi-parallel shock.